I wouldn't worry about the case too much. People do some absurd things with .357 magnum Freedom Arms 83s. Sometimes you hear it called .353 Casull (link below). Pressure can get to 60,000+ PSI. It'll ruin primer pockets in about one loading apparently, but not go catastrophic (in that bank vault revolver). As to whether you want to push a Ruger 77/357, that is up to you. I'm nearly certain it could handle hotter than standard loads since it is also chambered for .44 mag, but the tricky part would be HOW MUCH hotter and WHEN to call it a day.
http://www.sixguns.com/tests/tt353.htm
http://www.sixguns.com/tests/tt353.htm
